Yesterday Review¶

Sheet of paper is \(11''\) by \(8''\) corners are cut in a square fashion paper is bent to make rectangular prism Pasted image 20220825143955.png

\(V=hlw\) one inch cut out from the corner \(h=1, l=9, w=6\) |\(V(l)\)|\(l*l*w=Vin^3\)| |:-|-:| |\(V(0)\)|\(0*11*8=0in^3\)| |\(V(1)\)|\(1*9*6=54in^3\)| |\(V(1.5)\)|\(1.5*8*5=60in^3\)| |\(V(2)\)|\(2*7*4=56in^3\)| |\(V(3)\)|\(3*5*2=30in^3\)| |\(V(4)\)|\(4*3*0=0in^3\)| Domain: \(0<x<4\) \(V(x)=x(11-2x)(8-2x)\) \(V(x)=4x^3-38x^2+88x\) \(V'(x)=12x^2-76x+88\) \(0=12x^2-76x+88\) \(0=4(3x-19x+22)\) \(0=3x-19x+22\)

Derivative:¶

\(V(x)=ax^N\) \(V'(x)=aNx^{N-1}\)

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\(x=\frac{-b\pm\sqrt{b^2-4ac}}{29}\) \(x=\frac{-(-19)\pm\sqrt{(-19)^2-4(3)(22)}}{2(3)}\) \(x=\frac{19\pm \sqrt{361-264}}{6}\) \(x=\frac{19\pm \sqrt{97}}{6}\) |+|-| |-|-| |\(x=\frac{19+ \sqrt{97}}{6}\)|\(x=\frac{19- \sqrt{97}}{6}\)| |\(\approx9.8\)|\(\approx1.5\)|

Homework¶

make a graph